Gravitation - Kepler and Newton revision notes and calculations.

The first 200 words of this essay...

Gravitation

Kepler (1571-1630) has studied for many years the records of observation on planets and summarised three laws.

Kepler's Law

(1) Each planet moves in an ellipse which has the sun at one focus

(2) The line joining the sun and the moving planet sweeps out equal area in equal time

(3) the square of the time of revolution of any planet (i.e. T) about the sun is proportional to the cube of the planets' mean distance from the sun

I.e. is a constant

Interpretation form Kepler's laws

(I) Kepler's second law :

The area swept out in a very short time interval (?t), neglecting the

small triangular region is A

The rate of area swept =

Hence it is a constant.

Compare this equation with the angular momentum

= Constant

This law is in fact an evidence of conservation of angular momentum.

(II) Kepler's third law

About 1666, Newton investigated the motion of the moon, and thought that it was the force of gravity to pull the moon and keep it